The long-term objectives of this research are to further our understanding of the orgin of dynamic spatial patterns in chemically-reacting systems and to apply this knowledge to the analysis of specific problems of pattern formation in developmental biology. The specific objectives in this phase can be grouped into three categories. (1) Classification of kinetic mechanisms: (a) Determine the parametric response of steady-state and time-dependent solutions for some representative two-species in a nonuniform systems. (b) Develop experimentally-testable predictions as to how solutions of each of the generic types of two-species models behave under perturbations. (2) Time-dependent spatial patterns: (a) Determine whether any two-species kinetic model of the cross activation-inhibition type can give rise to finite amplitude propagating waves when the diffusion coefficients of the two species are equal. (b) Determine whether the spiral patterns observed in the aggregation phase of Dictyostelium discoideum and in the growth patterns of colonial fungi can be explained by an appeal to diffusive instabilities or whether some other pattern-formation mechanism must be invoked. (3) Graph-theoretic analysis of biochemical networks: (a) Analyze the local and global steady state and time-dependent flow on biochemical networks in spatically-uniform systems. (b) Extend the results of the analysis in (a) to nonuniform systems. Identify those types of network structure that never give rise to diffusive instabilities.